Une caractérisation des formes symplectiques
Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 265-280.

On montre qu’une 2-forme non nulle sur une variété M, telle que le pseudogroupe des difféomorphismes locaux la préservant soit transitif sur le fibré des directions tangentes, est symplectique si la dimension de M n’est pas 6. De plus, il y a un contre-exemple en dimension 6, dont on montre qu’il est essentiellement unique.

It is shown that a nonzero 2-form on a manifold M, such that the pseudogroup of local diffeomorphisms preserving it acts transitively on the bundle of tangent directions, is symplectic if dim M is not 6. Moreover, there is a counterexample in 6 dimensions, which is shown to be essentially unique.

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Sévennec, Bruno. Une caractérisation des formes symplectiques. Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 265-280. doi : 10.5802/aif.1618. http://archive.numdam.org/articles/10.5802/aif.1618/

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